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Search Results (6)

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Keywords = sublinear expectation space

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16 pages, 295 KB  
Article
Laws of the k-Iterated Logarithm of Weighted Sums in a Sub-Linear Expected Space
by Xiang Zeng
Mathematics 2025, 13(18), 3034; https://doi.org/10.3390/math13183034 - 20 Sep 2025
Viewed by 176
Abstract
The law of the iterated logarithm precisely refines the law of large numbers and plays a fundamental role in probability limit theory. The framework of sub-linear expectation spaces substantially extends the classical concept of probability spaces. In this study, we employ a methodology [...] Read more.
The law of the iterated logarithm precisely refines the law of large numbers and plays a fundamental role in probability limit theory. The framework of sub-linear expectation spaces substantially extends the classical concept of probability spaces. In this study, we employ a methodology that differs from the traditional probabilistic approach to study the k-iterated logarithm law for weighted sums of stable random variables with the exponent α∈(0,2) within sub-linear expectation space, establishing a highly general form of the k-iterated logarithm law in this context. The obtained results include Chover’s law of the iterated logarithm, as well as the laws for partial sums and moving average processes, thereby extending many corresponding results obtained in classical probability spaces. Full article
(This article belongs to the Section D1: Probability and Statistics)
32 pages, 367 KB  
Article
Laws of Large Numbers for Uncertain Random Variables in the Framework of U-S Chance Theory
by Xiaoting Fu, Feng Hu, Xue Meng, Yu Tian and Deguo Yang
Symmetry 2025, 17(1), 62; https://doi.org/10.3390/sym17010062 - 2 Jan 2025
Cited by 1 | Viewed by 713
Abstract
The paper introduces U-S chance spaces, a new framework based on uncertainty theory and sub-linear expectation theory, to depict human uncertainty and sub-linear features, simultaneously. These spaces can be used to analyze the characteristics of uncertain random variables and study investments and other [...] Read more.
The paper introduces U-S chance spaces, a new framework based on uncertainty theory and sub-linear expectation theory, to depict human uncertainty and sub-linear features, simultaneously. These spaces can be used to analyze the characteristics of uncertain random variables and study investments and other related issues in incomplete financial markets. Within the framework, sub-linear expectation theory describes the randomness in financial behaviors, while uncertainty theory describes the uncertainty associated with government macro-control or experts’ opinions. The main achievement of this paper is the derivation of the Kolmogorov law of large numbers for uncertain random variables under U-S chance spaces. Examples are provided, and the theorems can be applied to uncertain random variables that are functions of random variables with symmetric or asymmetric distributions and uncertain variables with symmetric or asymmetric distributions. In some cases, when both random and uncertain variables are symmetric, the limit in the law exhibits the form that is characterized by symmetrical uncertain variables. Full article
(This article belongs to the Section Mathematics)
16 pages, 2850 KB  
Article
Multi-Armed Bandit-Based User Network Node Selection
by Qinyan Gao and Zhidong Xie
Sensors 2024, 24(13), 4104; https://doi.org/10.3390/s24134104 - 24 Jun 2024
Cited by 1 | Viewed by 1357
Abstract
In the scenario of an integrated space–air–ground emergency communication network, users encounter the challenge of rapidly identifying the optimal network node amidst the uncertainty and stochastic fluctuations of network states. This study introduces a Multi-Armed Bandit (MAB) model and proposes an optimization algorithm [...] Read more.
In the scenario of an integrated space–air–ground emergency communication network, users encounter the challenge of rapidly identifying the optimal network node amidst the uncertainty and stochastic fluctuations of network states. This study introduces a Multi-Armed Bandit (MAB) model and proposes an optimization algorithm leveraging dynamic variance sampling (DVS). The algorithm posits that the prior distribution of each node’s network state conforms to a normal distribution, and by constructing the distribution’s expected value and variance, it maximizes the utilization of sample data, thereby maintaining an equilibrium between data exploitation and the exploration of the unknown. Theoretical substantiation is provided to illustrate that the Bayesian regret associated with the algorithm exhibits sublinear growth. Empirical simulations corroborate that the algorithm in question outperforms traditional ε-greedy, Upper Confidence Bound (UCB), and Thompson sampling algorithms in terms of higher cumulative rewards, diminished total regret, accelerated convergence rates, and enhanced system throughput. Full article
(This article belongs to the Section Physical Sensors)
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16 pages, 294 KB  
Article
Equivalent Conditions of Complete p-th Moment Convergence for Weighted Sum of ND Random Variables under Sublinear Expectation Space
by Peiyu Sun, Dehui Wang and Xili Tan
Mathematics 2023, 11(16), 3494; https://doi.org/10.3390/math11163494 - 13 Aug 2023
Cited by 1 | Viewed by 1217
Abstract
We investigate the complete convergence for weighted sums of sequences of negative dependence (ND) random variables and p-th moment convergence for weighted sums of sequences of ND random variables under sublinear expectation space. Using moment inequality and truncation methods, we prove the equivalent [...] Read more.
We investigate the complete convergence for weighted sums of sequences of negative dependence (ND) random variables and p-th moment convergence for weighted sums of sequences of ND random variables under sublinear expectation space. Using moment inequality and truncation methods, we prove the equivalent conditions of complete convergence for weighted sums of sequences of ND random variables and p-th moment convergence for weighted sums of sequences of ND random variables under sublinear expectation space. Full article
(This article belongs to the Special Issue Analytical Methods and Convergence in Probability with Applications, 2nd Edition)
16 pages, 316 KB  
Article
Moderate Deviation Principle for Linear Processes Generated by Dependent Sequences under Sub-Linear Expectation
by Peiyu Sun, Dehui Wang, Xue Ding, Xili Tan and Yong Zhang
Axioms 2023, 12(8), 781; https://doi.org/10.3390/axioms12080781 - 11 Aug 2023
Viewed by 1482
Abstract
We are interested in the linear processes generated by dependent sequences under sub-linear expectation. Using the Beveridge–Nelson decomposition of linear processes and the inequalities, the moderate deviation principle for linear processes produced by an m-dependent sequence is established. We also prove the upper [...] Read more.
We are interested in the linear processes generated by dependent sequences under sub-linear expectation. Using the Beveridge–Nelson decomposition of linear processes and the inequalities, the moderate deviation principle for linear processes produced by an m-dependent sequence is established. We also prove the upper bound of the moderate deviation principle for linear processes produced by negatively dependent sequences via different methods from m-dependent sequences. These conclusions promote and improve the corresponding results from the traditional probability space to the sub-linear expectation space. Full article
(This article belongs to the Special Issue Probability, Statistics and Estimation)
11 pages, 279 KB  
Article
The Law of the Iterated Logarithm for Linear Processes Generated by a Sequence of Stationary Independent Random Variables under the Sub-Linear Expectation
by Wei Liu and Yong Zhang
Entropy 2021, 23(10), 1313; https://doi.org/10.3390/e23101313 - 7 Oct 2021
Cited by 13 | Viewed by 2215
Abstract
In this paper, we obtain the law of iterated logarithm for linear processes in sub-linear expectation space. It is established for strictly stationary independent random variable sequences with finite second-order moments in the sense of non-additive capacity. Full article
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